allyabase (named for an early oughts internet meme, which featured the quirkily translated game Zero Wing) is a playful jab at the BaaS (backend as a service) platforms in name, and a serious attempt at providing public backend infrastructure in form. In addition to referencing a time when the internet was weirder, it is meant as a (playful) reminder that BaaS is a thinly veiled data collecting mechanism where you get to pay for the privelage of handing your user's habits to advertisers for them to profit off of. allyabase wants to be a free, open source, self-hostable alternative to whatever other BaaSes may be out there.
The README in the repo 
is probably the best place to get started.
But if you're more interested in how a network of allyabase servers can work then check out How Bases Work.
If you just want a brief overview of what miniservices exist, here they are:
addie - the accountant of the miniservices
aretha - a mini service for digital inventory and goods like tickets, cards, etc.
bdo - Big Dumb Object, for when you just need to store a bunch of json.
continuebee - For when you need to verify some local state
dolores - short-form video (under 1min or so)
fount - a MAGIC resolver, and character builder
joan - the service for account recovery mechanisms in allyabase
julia - the switchboard for allyabase
pref - preferences
sanora - need to sell something? Sanora's got you covered. Here's a little bit on Why Sanora Is Cool.
If you'd like to run your own base, you should check out Establishing A Base.